Frozen Lake , Uniform Stick.

A straight uniform stick of L= 1m and mass m = 1 KG lies on a surface of a frozen lake.Someone kicks the stick at one end,imparting an impulse of 2Ns normal to the stick.Describe the subsequent motion of the stick.

2. Relevant equations

I=mΔV

3. The attempt at a solution

Obviously the first thing we have to do is find the linear velocity at the end of the stick ( actually all molecules of the stick will be moving with that velocity). so I=m(V1-V0)

<=> 2=1*V1 , V0=0 since it was at rest.Therefore V1=2m/s which will remain constant due to lack of friction.The stick will be sliding forward since there are no forces to counteract with the initial force.But this force also created a torque which causes the object to rotate.

Should i assume that since there is no friction , the stick is rolling right from the beginning ? How can i find the angular velocity ?

I believe that since the kick is an external force and thus an external torque then linear and angular momentum are not conserved .

Well i already said the moment of inertia is ML/12 so i assumed that it is the centre of mass of the stick . Can i use it as a general rule and say that for any body which is free to move any force applied to it ( besides those who cross the axis of rotation of the CoM) will cause it to rotate about its CoM.

In terms of energies : Einitial = 1/2 ( Iω +mVcm) .

Why isn't Vcm = ωR ? Does this means that a particle at the end of the stick will cover more distance than the CoM in the same time t ?

Well i already said the moment of inertia is ML/12 so i assumed that it is the centre of mass of the stick . Can i use it as a general rule and say that for any body which is free to move any force applied to it ( besides those who cross the axis of rotation of the CoM) will cause it to rotate about its CoM.

a body rotates about its centre of rotation

(the clue's in the name! )

the formulas torque = Iα and torque of impulse = I(∆ω) only (and always) work about the center of mass and the centre of rotation …

in this case it isn't obvious where the centre of rotation is, so we use I and torque about the centre of mass …